12 Lens Calculator

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Milestone White Paper

Lens Calculations Do the Math

A step-by-step guide to lens parametersand calculations for video surveillancecameras.


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Milestone White PaperLens Calculations Do the MathA step-by-step guide to lens parameters and calculations for video surveillance.

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Table Of Contents

Introduction........................................................................................ 4The function of the lens............................................................... 5Sensor Format.................................................................................... 5The Iris (Diaphragm)..................................................................... 6Focal Length........................................................................................ 8Field of View........................................................................................ 8Magnification.................................................................................... 14Optical Speed: f-number............................................................ 14Depth of Field................................................................................... 15Calculating the depth of Field................................................. 16Milestone System........................................................................... 21


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Introduction

Today there is no technical reason why the image on an IP camera

should not be top quality. If there are problems with the image, it is

more than likely down to the lens not being the right one for the job.Selecting the right lens for the application is one of the most importanttasks in designing a surveillance solution. This article covers a step by

step process to do the math for lenses to help you select the best

lens so that your customer sees the best quality images, and providethem with the documentation to support your choice. To select the

best lens you need to take several factors into account:

Type of lens Amount of light required on the camera sensor

Format of the sensor

Focal length of the lens (FL)

Field of view (FOV)

Magnification (M)

f-number (f)

Depth of field (DOF)

There are many different types of lenses used for video surveillance

applications, probably the most common is a fixed focal length (FFL)video lens. This typically fitted with an automatic iris that optimizesthe amount of light that reaches the sensor to give the best quality

image. To cover a range of applications and fields of view (FOV) lenses

are available in:

Wide-angle (90)

Medium-angle (40)

Narrow-angle (5)

To cover a wide scene and have the ability to get a close-up with thesame camera you would use a variable FOV, vari-focal or zoom lens.

Using a vari-focal lens you can fine tune the focal length (FL) of the

lens for a specific application. A Pan/Tilt mechanism further increasesthe cameras FOV by allowing you to move the camera to viewdifferent scenes, a camera with all three functions, pan, tilt and zoom

is typically called a PTZ camera.

Author:

Eric Fullerton, Chief Sales and Marketing Officer, MilestoneSystems, the worlds leading innovator and thought leaderof open platform IP video management software.


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The funct ion of the lens

A lens is an optical device with perfect or approximate axial symmetry

which transmits and refracts light, converging or diverging the beam.

A simple lens consists of a single optical element. A compound lens ismade up of an array of simple lenses (elements) with a common axis.By using multiple elements allows the lens manufacturer to correct

more optical aberrations than is possible with a single element.

Manufactured lenses are typically made of glass or transparent plastic.

The lens in a surveillance camera focuses an image of the scene onto

the camera sensor. Camera sensors come in a variety of formats and

the correct lens must be used to get the best results from each format.

Sensor Format

In IP surveillance cameras, the sensor format is the shape and size of

the image sensor. The sensor format determines the angle of view of aparticular lens when used with a particular camera. Larger image

sensors capture images with less noise and greater dynamic rangethan smaller sensors. Both the signal-to-noise ratio and sensor unitygain are proportional to the square root of image sensor area.

The EIA and NTSC standards define that all surveillance sensorformats have a horizontal by vertical geometrical ratio of 4 x 3. There

are three popular sensor formats that you will find in surveillance

cameras: , 1/3 and .

Figure 1: Sensor Format


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The sizes (labels) used to reference the type of sensor format do not

correspond directly to the actual size of the sensor, in each case the

actual dimensions of the sensor are a little smaller. These labels arederived from the original Videcon television tube used in early TVcameras that had a 1 diameter tube with an actual scanned area

(active sensor area) of about 16mm in diameter.

Figure 2: Videcon Television Tube

The early labels for the sensor sizes have stuck with the industry. The

actual dimensions for use in calculations of each sensor format aregiven in the table below:

Any lens designed for a larger sensor format can be used with a

smaller sensor format, but the opposite is not true. For example, alens designed for a 1/3 sensor will not work correctly on a sensor

format, it will produce vignetting, a dark area surrounding the image.

The Iris (Diaphragm)

Behind the lens there is an iris or diaphragm. An iris is a thin opaque

structure with an opening (aperture) at its centre. The size of the

aperture regulates the amount of light that passes through the lens tothe sensor. The centre of the iris aperture coincides with the optical

axis of the lens system.


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Figure 3: A Six-Blade Iris

The iris consists of a series of overlapping metal leaves that open andclose to control the amount of light that reaches the sensor. A video

camera lens has a mechanical iris function in which a motorautomatically opens and closes the iris aperture to optimize the imagefrom the camera. The iris motor is controlled by the video signal

output from the sensor.

Figure 4: Iris Aperture Positions


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Focal Length

The focal length (FL) of a lens is a measure of how strongly it

converges (focuses) or diverges (diffuses) light. This is known as

optical power and a lens with a short focal length has greater opticalpower than one with a long focal length.

Figure 1: The focal point (F) and focal length (FL) of a positive(convex) lens and a negative (concave) lens

For a thin lens in air, the focal length is the distance from the center of

the lens to the principal focal point of the lens. In a surveillancecamera the surface of the image sensor is placed at the focal point of

the lens.

For a converging lens (for example a convex lens), the focal length ispositive, and is the distance at which a beam of parallel light will be

focused to a single spot. For a diverging lens (for example a concavelens), the focal length is negative, and is the distance to the point from

which a parallel beam appears to be diverging after passing throughthe lens.

Field of View

In surveillance, the field of view (FOV) is that part of the scene that isvisible through the camera at a particular position and orientation inspace. Objects outside the FOV are not recorded, this becomes

important when gathering evidence.

Although related, FOV is not exactly the same as angle of view (AOV).FOV is measured in linear dimensions (feet, inches, meters, etc.), AOV

(more properly called the angular field of view) is measured in

(dimensionless) degrees of arc. FOV increases with distance, AOV doesnot. FOV changes as the camera rotates, AOV does not. So, while AOV

is useful for lens design, FOV is more useful for you in designing asurveillance solution.

Calculating the field of view helps you select the appropriate camera

(sensor format) and lens for a surveillance task. Note that whilecommercial video lenses are constructed from multiple elements, thesimple lens shown in the diagram has the same effective focal length.


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Using simple geometry the scene size seen by the sensor is inversely

proportional to the lens focal length (FL). The diagram shows the

projected image on the sensor (h) of the scene (H) at some distanceD. Using similar triangles we can calculate the vertical angle of view Hand then vertical angle of view h.

Figure 2: Side View for Vertical Field of View (FOV) Calculation

The vertical AOV h is then calculated using trigonometry.


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For the horizontal FOV:

Figure 3: Plan View for Horizontal Field of View (FOV) Calculation

The horizontal AOV w is then calculated using trigonometry.

Refer to the FOV tables for the AOV and scene sizes for lenses of

different focal length and distance to scene.


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Field of view and scene sizes for sensor format


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Field of view and scene sizes for 1/3 sensor format


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Field of view and scene sizes for sensor format


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Magnification

Optical magnification is the ratio between the apparent size of an

object (or its size in an image) and its true size. For surveillance

applications the overall magnification of a specific camera lens andmonitor size depends on:

Lens focal length FL

Sensor format

Monitor size

Because surveillance cameras have a fixed size of sensor the camera

can only see as much of the image as will fit on its sensor. Themagnification at the camera Ms is related to the focal length FL and thediagonal of the sensor d:

When the image is displayed on a monitor it is magnified again. The

magnification at the monitor Mm is related to the monitor diagonal dm

and the sensor diagonal ds:

The combined magnification of the lens and the monitor is then:

Optical Speed: f -number

The f-number (sometimes called focal ratio, f-ratio, or relative

aperture) of a lens is the focal length (FL) divided by the "effective"aperture diameter (d). It is a measure of how much light the lens

collects and transmits to the sensor. It is also called the lens speed oroptical speed.


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As the focal length of a lens increases the aperture diameter must

increase proportionately to keep the f-number the same. The same

relationship applies to the amount of light transmitted to the sensor,for example, an f/2.0 lens transmits four times as much light as anf/4.0 lens with the same focal length.

Figure 4: Decreasing apertures, increasing f-numbers

The diagram shows decreasing apertures, that is, increasing f-numbers, in one-stop increments. Each aperture transmits half the

light to the sensor as the previous one. The actual size of the aperturewill depend on the focal length of the lens. The more light the lens cancollect and transmit to the sensor, the better the contrast and imagequality will be. A large lens collects more light and therefore permits

the camera to operate in lower light levels.

Most lenses have an iris ring marked with f-numbers such as 1.4, 2.0,2.8, 4.0, 5.6, 8.0, 11, 16, 22, C. The difference between each stop is a

factor of 2 in the light transmitted by the lens. Changing the f-number

from f/2.0 to f/1.4 doubles the amount of light transmitted to thesensor by the lens. C indicates that the iris is closed and no light is

transmitted.

Depth of FieldThe depth of field (DOF) is the portion of a scene that appears sharp in

the image on the sensor. Although a lens can precisely focus at onlyone distance, the focused distance, the decrease in sharpness is

gradual on either side of the focused distance, so that within the DOF,

you see the image as in focus under normal viewing conditions.

Figure 5: A view with a shallow depth of field


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The DOF is determined by the focused distance (the distance to the

plane that is perfectly in focus), the focal length, and the f-number.

Calculating the depth of Field

To calculate the depth of field at a specific focus distance we first need

to know two characteristics for the sensor and the lens: The circle of confusion for the sensor

The hyperfocal distance for the lens

Circle of Confusion: with any lens a precise focus is possible at only

one distance, the focus distance. At the focus distance, a point objectwill produce a point image. At any other distance, a point object isdefocused, and will produce a blur spot shaped like the aperture

(circular). When this blur spot is sufficiently small, it is

indistinguishable from a point, and appears to the eye to be in focus,we say it is acceptably sharp. The diameter of the blur spot increaseswith distance from the point of focus and the largest diameter blur

spot that is indistinguishable from a point (seen by the eye as focused)is known as the circle of confusion.

The diameter of the blur spot increases gradually so the limits of depth

of field are not hard boundaries between sharp and unsharp. The area

of the scene within the depth of field appears sharp (to the eye) andthe areas in front of and beyond the depth of field appear blurred.

We can use the Zeiss formula to calculate the circle of confusion (c):

where d is the diagonal of the sensor. The table below shows the value

of c for the common sensor formats used in surveillance cameras.

Hyperfocal distance: is the nearest focus distance at which the DOF

extends to infinity. Focusing the camera at the hyperfocal distanceresults in the largest possible depth of field for a given f-number.

Focusing beyond the hyperfocal distance does not increase the far DOF

(which already extends to infinity), but it does decrease the near DOFin front of the subject, so overall this would decreas the total DOF.


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The hyperfocal distance H is given by:

Where FL is the focal length of the lens, f is the f-number, and c is the

circle of confusion for the sensor format.

Calculating the depth of field: when the camera is focused on asubject at distance s, where s is large in comparison with the focal

length of the lens, the distance from the camera to the near limit of

the DOF Dn and the distance from the camera to the far limit of theDOF Df are:

the near limit

the far limit

The depth of field Df Dn is:

For the case when s is the hyperfocal distance,

and

As you can see for s H, the far limit of the DOF is at infinity and theDOF is infinite and in this case only objects at or beyond the near limit

Dn of the DOF will appear with acceptable sharpness.

Substituting for H and rearranging, the DOF can be expressed as:

On the following pages, we provide some depth of field tables.


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Milestone System

Innovator.Milestone Systems is internationally recognized as an

innovator and thought leader in open platform IP video management

software. Milestones XProtect products operate as the core ofsurveillance systems: connecting, sharing and managing all devicesthrough a single interface that is easy to learn and operate.

Easy to use.The XProtect platform is easy to use, proven in operationand scales to support unlimited devices. XProtect products support thewidest choice of network video hardware and are designed with an

Application Programming Interface (API) that integrates seamlessly

with other manufacturers systems.

Best-of-breed.Using XProtect, you can build scalable, best of breed

solutions to reduce cost, optimize processes, protect assets and

ultimately increase value in a companys products and services.

Copyright Milestone Systems 2009


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Milestone Systems is the industry leader in developing true

open platform IP video management software. TheXProtect platform gives users a powerful surveillance

solution that is easy to manage, reliable and proven in morethan 50,000 customer installations worldwide.

With support for the industrys widest choice in networkhardware and integration with other systems, XProtect

provides best-of-breed solutions to video enable

organizations reducing costs, optimizing processes, andprotecting assets.

Milestone software is sold through authorized partners in

over 90 countries.

Office Locations:

Milestone Systems Inc.

8905 SW Nimbus Avenue, Beaverton, OR 97008, United StatesTel: +1 (503) 350 11000

Milestone Systems A/S (Headquarters)

Banemarksvej 50, 2605 Brndby, DenmarkTel: +45 88 300 300

Milestone Systems DE

Am Kleefeld 6a, D-83527 Haag i.OB., Germany

Tel: +49 (0) 8072 442173

Milestone Systems Italy

Via Paisiello,110, 20092 Cinisello Balsamo, Milano, ItalyTel: +39 02 6179 508

Milestone Systems UK, Ltd.118 Codnor Gate, Ripley, Derbyshire DE5 9QW, Great BritainTel: +44 (0) 1773 570 709

Milestone Systems France121 rue d'Aguesseau, 92100 Boulogne-Billancourt, FranceTel: +33 141 03 14 82

Milestone Systems Japan

c/o Royal Danish Embassy, 29-6, Sarugaku-cho, Shibuya-ku, Tokyo 150-0033, JapanTel: +81 (0)3 3780 8749

Milestone Systems Pte. Ltd.30 Robinson Road, 13-03 Robinson towers, Singapore 048456Tel: +65 6225 2686

Milestone Systems Middle EastP.O, Box 500809, DIC, Building 5 IEB, 6th floor Office 606, Dubai, United Arab Emirates

Tel: +971 50 8827093

Corporate website: www.milestonesys.com

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